Geometric algebra in electrical engineering: a comprehensive review of power systems applications.

This review provides a comprehensive overview of the applications of geometric algebra (GA) in electrical engineering, with a particular focus on power systems. The paper covers the fundamental concepts of GA and its advantages over traditional mathematical approaches in power system analysis. Key topics explored include: an introduction to GA and its relevance to electrical engineering; AC circuit theory using GA, covering GA formulations for power flow analysis in non-sinusoidal conditions including harmonic and interharmonic analysis for single-phase and multi-phase systems; power-free current compensation techniques that move beyond traditional reactive power concepts; parameter identification in electrical circuits using GA; GA-based perspectives on electrical transformations (Clarke or Fortescue) and the analysis of electrical curves and their geometric invariants. The review synthesizes recent advancements, including contributions from the authors and colleagues, discusses future directions and highlights the potential of GA to address current and emerging challenges in power system analysis, control, smart grids and renewable energy systems. We aim to provide both a theoretical foundation and practical insights for researchers and practitioners in the field. This article is part of the theme issue 'Modern applications of geometric algebra'.